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• Aim: What is the Law of Cosines and how can we apply it? (This formula will be on the Regents Reference sheet)

At the end of this lesson, you will be able to...

1. explore and discover the Law of Cosines
2. express the Law of Cosines in various ways
3. solve problems using the Law of Cosines
4. compare and contrast the conditions necessary to use the Law of Cosines as opposed to the Law of Sines

Not all triangles can be solved using the Law of Sines. so the Law of Cosines was invented to help solve triangles that the Law of Sines cannot. Hwere are two videos that explain the Law of Cosines. The Law of Cosines has three forms. The Regents Reference table only gives one form.

Copy these questions into your notebooks and answer them as you watch the videos

1. What are the three forms for the Law of Cosines?
2. What triangle information do you need to know in order to use the Law of Cosines?


Video 1



Video 2

• Classwork: Solve each problem. Be sure to draw a picture for each before you solve.

1. In triangle ABC, AB = 8, AC = 10, and the cos A = 1/8. Find BC. (Ans: BC=12)
2. In triangle DEF, d = 12, e = 8 and f = 6. Find cos C. (Ans: cos C = 43/48)
3. The diagonals of a parallelogram measure 12 cm and 22 cm and intersect at an angle of 143°. Find the length of the longer sides of the parallelogram to the nearest tenth cm. (Ans: The longest side measures 16.2 cm)

• Homework: For each do in multiples of four. The first two pages solve for a side. The last two pages are solving for an angle.

Law_of_Cosines,_1.JPG

Law_of_Cosines,_2.JPG

Law_of_Cosines,_3.JPG

Law_of_Cosines,_4.JPG

• Answers:

A-Law_of_Cosines.JPG

• Journal entry: After using the Law of Cosines to find a missing angle of a triangle, Barbara determined that cos A=1.75. What conclusions can you draw about the triangle?